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For any integer n greater than 1, [n denotes the product of
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17 Aug 2020, 10:34
17 Aug 2020, 10:34
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For any integer n greater than 1, [n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between [6 + 2 and [6 + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Re: For any integer n greater than 1, [n denotes the product of
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17 Aug 2020, 10:34
17 Aug 2020, 10:34
Expert Reply
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Re: For any integer n greater than 1, [n denotes the product of
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17 Aug 2020, 11:27
17 Aug 2020, 11:27
Carcass wrote:
For any integer n greater than 1, [n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between [6 + 2 and [6 + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
(A) None
(B) One
(C) Two
(D) Three
(E) Four
[6 + 2 = (6)(5)(4)(3)(2)(1) + 2 = 2[(6)(5)(4)(3)(1) + 1], which is a multiple of 2. So, [6 + 2 is NOT prime
[6 + 3 = (6)(5)(4)(3)(2)(1) + 2 = 3[(6)(5)(4)(2)(1) + 1], which is a multiple of 3. So, [6 + 2 is NOT prime
[6 + 4 = (6)(5)(4)(3)(2)(1) + 2 = 4[(6)(5)(3)(2)(1) + 1], which is a multiple of 4. So, [6 + 2 is NOT prime
[6 + 5 = (6)(5)(4)(3)(2)(1) + 2 = 5[(6)(4)(3)(2)(1) + 1], which is a multiple of 5. So, [6 + 2 is NOT prime
[6 + 6 = (6)(5)(4)(3)(2)(1) + 2 = 6[(5)(4)(3)(2)(1) + 1], which is a multiple of 6. So, [6 + 2 is NOT prime
Answer: A
Cheers,
Brent
